You are misunderstanding the sim issue. The only thing locked about the sims is that once the sim has been powered up in a phone, it gets imprinted with the phone's serial number. If you put the sim in another phone, it will know it is in the wrong place and will reject. Even if you have a brand new never powered-up sim, it could still be registered in TF's system as belonging to a particular phone and won't work in another phone. It won't say reject, but it won't work. This is how new phones are sold. You don't have to provide the sim number because they already know it. If you have a used phone and want to change the phone number, that is another case where the sim can be used only once for a number and TF will send a new sim for free. So all you have to do is sell the phone with the understanding that it is used, so TF will have to send a new sim for the new phone number. Also, it will need a new sim because of being deactivated past the cutoff time, two months I think.
There is no way to remove your phone number info from the phone. It will roll over when a new one is added. If you had the phones in an online account, remove them. In order to remove the remaining one, you have to call CS.
When you call CS about stuff, they ask for your name for verification. Either tell your customer to use your name or else ask CS to change your name to the new person's name. There might not be a name there at all in the first place. It depends if you called CS for help in the past.